I have read a number of websites to figure out how to calculate the recipes for the batter amounts as per the cake pan sizes ie 6”, 7” etc. Nothing so far I have read tells you neither how to fomulate a recipe nor gives a recipe as per the size of cake pans.
My mind is utterly confused with all this information and have no clarity on this issue.
How does one decide on a recipe amount for a 6” cake with two layers or an 8” cake with two layers?
I do not have formal training in baking but I am very passionate about baking and I experiment a lot. I wish to pursue this as a business, but these calculations are completely consuming my mind and do not know where to begin if I wanted to do a recipe chart for different sized cakes that would be the foundation for starting out.
I would really appreciate help into this matter.
Thanks!
Regards

The formula that you mentioned is Pi R2 that is the area of the circle if my understanding is right. I am still unable to understand.
Let me give an example and maybe it can simplify what I am trying to understand:
Suppose there is a recipe that calls for an 8” pan, how does one alter/increase that if one has to bake a 9” cake.
Thanks!

Assuming the sides of both pans are the same height (such as 2”), you divide the 9” circle area by the 8” circle area and that will give you factor to multiply all the ingredients by.

Another way to do it is to use pan volume: an 8” pan holds 7 cups and a 9” pan holds 8.67 cups, so 8.67 /7 = 1.24, so you multiply all the ingredients for an 8” pan by 1.24. Make sense?

I highly recommend the back section of the Cake Bible, where there is a system to formulate batters for any size pan. The system is more complicated than simple scaling, because for butter cakes leavened with baking powder/soda you also need to change the leavening when pan size changes to avoid doming or dipping.